We prove an asymptotic formula for F(1/4-it+ir,1/4-it-ir,1/2;x ) as r, t→∞ and α=r/t→0. This special case of the Gauss hypergeometric function appears in the explicit formula for the first moment of Maass form symmetric-square L-functions.
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Dmitry Frolenkov (2024) studied this question.
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